In the representation of numerical data, a floating point representation can reduce the numbers of digits presented, that is, the order more than a fixed point representation and, in case of representing the bit of same number, the larger integer or the smaller decimal can be represented. Also, the floating point representation occupies a small space of memory unit, is easy to process and move within a central processing unit, and can improve the accuracy of the data representation with a limited number of bits.
The input data form of an adder circuit using the floating point representation consists of a mantissa sign bit, an exponent bit, and a mantissa bit, and an initial decimal point is fixed just in front of the first bit of mantissa.
The representative method of an exponent uses the type which adds a biased value to the value which is to be represented, and the representative method of a mantissa uses the type of a sign and absolute value.
Considering an operating principle of a K-bit floating point adder circuit, first the exponent magnitude of the two numbers is equalized by comparing the exponent magnitude of the two numbers which is to be added and shifting the mantissa of the number having the smaller exponent to the number of digits that equals the difference of the two exponents.
Then, the mantissa parts of the two numbers whose exponent magnitude is equalized, are added to become a mantissa output, and, however, the mantissa output is normalized by shifting the maximum effective bit of the mantissa output to the first bit position of the mantissa.
On the other hand, the exponent output is the value which adds the carry that is generated when the mantissa signs of the two numbers are same and the exponent whose magnitude is larger at the input, and subtracts the reduced value of the exponent which is generated in the normalization.
The processing speed of a floating point adder circuit becomes a very important problem when using an adder circuit of the above floating point representation in applications which requires high transform speed, such as real time image signal processing or phonetic signal processing.